Tank



y 31, 1951 A. l. CAQUOT 2,562,602

TANK

Filed Oct. 2, 1946 INVENTUR AL 55/67 IKENEE (AQUOT ATTURNEYO Patented July 31, 1951 'ascasczf i V ICE v i TANK Albert Irne Cannot, Paris, France Application October 2, 194 Serial No. 700,775

In France August 23,1946 1 r Such-bodies, and in particular tanks, are known s;

in whichthe wall,,generally a; metallic one,;isreinforced, either ,on'the inside or on the outside, by frames adapted to resist the more or less variable stresses resulting from. the combination of pressures due to the pressures exerted by the liquid and gas present inside the tank,

On the other hand, tanks arealso known, as described in the-French patent applications filed by Caquot and Dubois, on July 3, 1942for: Improvements Brought to Tanks, in Particular to Stationary Tanks for Liquidsv .and on October .2, 1942, for: Improvements Brought to Tanks, in Particular for Liquids, in which the stresses applied to the wall. of the tank are transmitted to anexternal belt or band carried byrs'upports suitably inclined for adapting themselves to expansion, both-radial and vertical, of the tank structure and also arranged to be able to absorb the resultants of the distinct stresses applied to the two main portions of the tank, to wit the dome or upper half and the cup-shaped portion or lower half. In particular, these supports are adapted to resist the-action of the resultant of the tractive stresses-that are created under certain conditions of partial filling-by the liquid, when the tank bottom resists directly upon the ground.

In certain embodiments of the tanks described in these prior patent applications, the upper portion of the dome wall was free from anyreinforcement on the inside, but this wallwas always supported, on the outside, by frame elements or byla concrete cap adapted to receive the Whole or a part of the compression stresses and to transmit them to the belt or band. 1 The object of the-present invention is to simplify the construction of the tanks or hollow bodies disclosed in these prior patents.

, A preferred embodiment of my invention will be hereinafter described with reference to the accompanying drawings, given merely by way of example, and in which: 7

Fig. 1 is an elevational view of an ovoid tank for liquid and gas (for instance intendedtocontain gasoline or the like, under pressure) made according to my invention;

Fig. 2 is a vertical section of this tank;

Fig. 3 is a sectional view on the line III-III of Fig. 2.

As above stated, the tank (or other hollow body) according to my invention includes a thin wall (of steel, aluminium, copper, etc., and possibly of concrete), of fiat ovoid'shape, supposed to be supported on the one hand, either directly or indirectly, through its bottom I, on the ground XX, and o e ot e and! r ushii h nt er.

tion of maximum area, on a belt or band 2 supported'by a plurality'of pillars3 capable of eventually resisting tractive stresses and anchored in the ground at 4.

Up to the present time, it was considered that the wall of such a tank had to be fitted with external reinforcing means in order to be able of resisting the stressesdevloped under certain con: ditions.

According to an essential feature of my invention, the wall of ia tankoi this kind, and especially the dome portion thereof, is free from any such reinforcementfand is shaped to resist by itself all stresses as may be applied thereto.

:In tanks of the type above set forth, in order to utilize the matter under the best possible conditions, the dome 5 is given the general shape of a body of revolution about a vertical axis ZZ and it iscalculated in such manner that the maximum stresses are, tensile stresses limitedto the same value bothon themeridians (sections by axial vertical planes) as on the parallels (sections by horizontal planes), these stress maximums being not as a rule simultaneous and, resistance calcu: lation being efiected through the conventional methods relating to double curvature surfaces.

But if the desired result can easily be obtained when the tank is wholly or nearly. wholly filled with liquid, the conditions are very diiTe'rent when the tank isonly partly 'filled,,with a gas pressure above the liquid level.

In thi ,case,;the wallof dome 5, supposed to be r of the shape shown in vertical section at dmb (Fig. 2), tends, under theefiect of the gaseous pressure, to deform by being inflated at the top (for instance, with a very great exaggeration, to-

ward the spherical surface am'lb). I nithetop portion of the dome, the main stresses are ten-' sions exerted on the parallels and the meridians. But the deformation of thedome produces a different effectupon the portion of the domeclose to belt}.v Inztihis portion of the tank, the stresses on the meridians .are compression stresses. In other words under the efiect'of the above mentioned deformation ofthe dome, the parallels in this lower portionthereoftend to shorten... These parallels, are located in a zone such as that between horizontal sections AB and CD (Fig.2), where, due to the general'ovoid shape that has been chosen, the curvaturesfof the meridians are max m m At a pointsuchas :v of this zone, Imay thereforehave, in the direction of the meridian and acting on the parallel, tensible stresses T1, and, on the contrary, in the direction of the parallel and acting-Lon the meridian, compression stresses T2 (Fig. 3). These compressions tendtoproduce a buckling effect which would correspond to deformations, such as fshown on an exaggerated scaleatfi onlfig. 3, l

Thus, in the zone between AB and CD, a buckling effect is produced which is due to the importance, of the meridian curvature. But, on the other hand, the increase of this meridian curvature tends to increasethe resistance to buckling. The principle of my invention consists in taking advantage of this circumstance for ob taining a structure which is capable of supporting the stresses exerted thereon in service without requiring external reinforcements.

As a matter of fact, the resistance to buckling of double curvature thin walls depends essentially upon the mean curvature Cm which is given by the following formula:

i v V p 1 '"(R,,2 1a,,2) in which l V R "is the curvature along the meridians and V l V R9 is the curvature along the parallels.

It is therefore possible, either by calculation or by successive trials, or by experimenting on models, to determine the meridian curve, in its portions ac or M corresponding to the zone in question, in such manner that the mean curvature, along these portions, gives rise to a resistance to buckling sufficient for enabling the wall tank to resist all stresses as maybe developed, even when the tank is but partly filled and sub- "jected to an internal pressure, without requiring any external reinforcement.

This will involve the choice, for the radius R bf curvature R1 of the meridians in said zone, of a certain value or acertain law of variation capable of ensuring the desired resistance to buckling. Of course, these values may vary within a certain range. It should be well understood that although the tank wall is capable of supporting by itself any stresses as may be produced, my invention does not exclude the provision of external reinforcements, intended for instance to ensure an increased margin of safety. a -There exists in the top portion of the dome (portion cmd) another cause of secondary compression stresses, resulting from negative pressures inside the tank, from the weight of the dome and from overloads due to climatic or accidental conditions. This secondary effect is of comparatively small importance and can easily be remedied if said portion cmd of the tank is given a shape approximateing that of a, portion of a sphere, with a radius R2 equal to or smaller than the value corresponding to buckling.

Concerning now the portion of the tank located under the belt and more especially the zone 1 between said belt and the bottom proper l, the phenomena that take place therein are analogous to those above referred to, but they are due to another cause, to wit the effect of the liquid alone during the filling or emptying of the tank.

If, for instance, it is supposed that the liquid level is at PQ, below the plane AB of belt 2, and that the gas pressure is low or equal to atmospheric pressure, zone aa'bb between AB and PQ tends to deform under the effect of the weight of the liquid, curvilinear arcs ad and bb tending to become straight lines so that in an intermediate plane such as EF buckling phenomena a suitable-choice of the mean curvature of portion 1, at "each of the'points of its meridians.

In other words, it will be necessary suitably to determine the radius or radii of curvature Rs of the curvilinear generatrix corresponding to this portion 1 of the tank.

Thus, it is possible for someone skilled in the art, by applying the principle of my invention and suitably determining parameters R1, R2, R3, etc., to obtain a, thin wall tank capable of resisting all the stresses that may be developed therein without requiring a reinforcement external frame. The values found for these parameters will generallylead to the choice of corresponding suitable values for therespective heights hi and hz of the dome and of the lower portion of the tank and also for the diameter d of the bottom in contact with the ground. This last men'- tioned value is preferably chosen large so as to reduce the effort applied to belt 2 and pillars 3 by the weight of the liquid in the tank.

Concerning the calculations leading to the choice of these values, the following indications are given, although it should be well understood that they have no limitative character. These indications relate, for instance to portion lot the tank and concern the eiforts in the vicinity of the belt (for instance in a plane such as PQ or EF) (Fig; 2). a

I will call: a v the annular volume per radian between the horizontal plane of the point that is being considered, the cylinder of a diameter. d equalto that of the bottom proper coaxial with the tank,

and the tank wall, i

w the specific weight of the liquid,

I s the annual area per radian in the horizontal plane of the point that is being considered, and

p the pressure in this horizontal plane.

The main effort Np per unit of length of the wall on the parallels, generally tension, will be given by the following formula:

' 5v+'sp r cos oz in the a is the angle of the plane tangent to the wall withv the vertical direction and r is the radius of the parallel.

' 0n the other hand, the main effort Nm on the meridian is given by the following formula:

by way of examples, these formulas will be applied to the case of a tank of a capacity of 10,000 cubic meters, in which I will consider a horizontal plane defined by the following values:

considered. It is found that the conditions thus obtained are much more favorable than for a cylindrical tank of the same radius R, for which calculation, shows that tension Nm would be equal to 194 tons per meter.

- I will now examine, according to the above explanations, the case in which these efforts Np and N111, or at least Nm, may be compressions. In order to calculate the maximum compression that may take place in the plane that isjconsidered (PQ or EF), it must be. supposed thatthe pressure becomes zero; in this case, in the-above example, I have:

Np=5.32 tOI1S per meter, and Nm=23.5 tons per meter.

Thus, while Np is still positive, Nm is negative. It corresponds to a compression whichmay involve a buckling effect.

Now, in order for the whole to resist buckling, the following condition must be complied with:

in which E is Hookes modulus, b Poissonscoefiicient, e the thickness of the wall andCm the above defined means curvature.

For a wall of 8.5 mm., this condition is:.

Nm 187 tons per meter.

So that, for a wall of a thickness of 8.5 mm., I have a safety coefficient equal to and with a gas pressure of 1.75 tons persquare meter, I have:

Np=16.1 tons per meter Nm=14.2 tons per meter.

Therefore, in this case, Nm corresponds to a compression. Now, resistance to buckling, according to the above formula, is sufficient when Nm is smaller than 159.4 tons per meter. Therefore, the safety coefficient is 1 On the other hand, the dome should, of course,- be capable of resisting the maximum main tensions corresponding to the case where liquid alone would fill the tank to the maximum level, with, in addition, the gas pressure. In the case above referred to, it would be found, by applying Formulas A and B, that these maximum tensions Nm and Np would not exceed '90 tons per meter, a value which can be supported, without any risk, by a wall 3.5 mm. thick. v

Finally, there would remain to verify, stillby means of the conventional formulas relating to buckling, that the dome can resist buckling under the effect of its own weight and of an overload. It would be easy to show that,-for a radius of curvature of for instance 21.40 in all directions and an overload of 0.65 ton per meter, the compression effort would average 6.95 tons per minute, corresponding to a safety coefficient of about 6. These examples show that it is possible, either through the calculation method. aboveset forth or through any other suitable method, to provide a thin wall tank the meridian of which is so shaped as to enable it to resist all stresses, both compression and tensile ones, that may be exerted thereon, without requiring any external reinforcement.

a It seems that, concerning the above mentioned parameters R1, R2, R3, and ratios 5%: and they should advantageously be chosen inside the following limits, which are given merely byway of indication but should not be considered as having any limitative character.

' hould preferably range from l.5 to 4;

' from 0.5 to 0.5;

from 0.15m 0.5

from 1 to 2.5 d

from 0.12 to 0.4.

Myv invention further includes the following features, relating more especially to the-belt and its-supports, on the one hand, and the C0llSt1llC-.

tion of the ovoid wall, on the other hand.

Concerning the belt, it has already been stated that its essential function is to act as a rigid support for the .thin wall of the tank proper. But it further contributes in protecting the tank against buckling and against deformation in the plane of its maximum horizontal section, in particular under-the effect of a lateral wind (if the reservior is not buried in the ground). The transverse section of this belt will thereforebe chosensufiiciently rigid and sufficiently strong for preventing any such deformation.

On the other hand, it is necessary, while .permitting displacements due to thermal expansion; to prevent any translatory movement of the belt (in particular under the action of wind).

In order to ensure expansion, the pillars such as 3' may be given a suflicient inclination, as al-v ready mentioned in the above mentioned prior applications, said pillars being arranged in such manner as to be able to move with respect to their base or to deform elastically. It is thus possible to guide the belt in such manner as to permit vertical displacements and radial deformations thereof.

In order to prevent horizontal displacements of the center of the belt in its own plane,-I provide bracing means, consisting for instance in a triangulation system *8 extending between the successive pillars 3 or at least some of them. The bracing means maybe constituted by the pillars themselves, disposed in V arrangement in eleva- In the embodiment shown by the drawings, p'illa'rs 3 are anchored, at the bases thereof, in concrete'or-metal blocks 4 (in which 'they may be pivotally mounted) these blocks beingcalculated aseaeoa 7- in such manner as to be able to resist the pressure of the pillars and being anchored at a sufficien't depth for resisting the traction that is exerted on these pillars under certain conditions of partial filling.

Of course, the supporting means for pillars 3 is not necessarily constituted by a plurality of elements such as said blocks 4. It might consist of a single annular element'suitably embedded in the ground. Concerning the construction of the reservoir proper, supposed to be constituted by metal sheets, I advantageously proceed by assembling (through riveting, welding or equivalent methods) developable elements, of suificiently small dimensions for making practically negligible the difference between the shape obtained after assembly and the theoretical shape, the assembled elements being themselves fixed to belt 2.

For instance, as shown in plane view at 9 on Fig. 3, these elements are made of substantially triangular shape.

Advantageously, according to a feature of my invention, the structure obtained after assembly of these elements is subjected to the action of an inner pressure (liquid pressure or gas pressure) sufilciently high for deforming the whole into a shape sufficiently close to the theoretical shape.

The tank wall is advantageously made of metal, but my invention does not exclude the use of other materials such as concrete, wood, etc. Also, while, in the above description, the tank has been supposed to be in the shape of a body of revolution about a vertical axis, my invention also applies to tanks the horizontal sections of which are of non-circular shape, for instance ovoid or elliptic.

Tanks made according to my invention have many advantages the most interesting of which are the following ones:

Their construction is cheap, owing to the possibility of dispensing with external reinforcing elements, and also owing to the fact that the material of which the walls are made are caused to work under the best possible conditions.

Their flat shape reduces the action of wind thereon when they are built above the ground and is particularly advantageous in the case of buried tanks. Furthermore, it permits of building tanks on grounds of relatively low resistance.

In a general manner, while I have, in the above description, disclosed what I deem to be practical and eflicient embodiments of my invention, it should be well understood that I do not wish to be limited thereto as there might be changes made in the arrangement, disposition and form of the parts without departing from the principle of the present invention as comprehended within the scope of the accompanying claims.

What I claim is:

l. A reservoir for holding a liquid at a variable level and under pressure of a gas, the pressure resisting part of said reservoir being constituted exclusively by a thin wall defining a space in the shape of a flattened spheroid and res-ting on the ground, a rigid belt spaced above the ground COD: nected on the outside of said wall substantially at the plane of maximum horizontal cross-section thereof, and anchoring means connecting said belt to the ground and assuring the immovability thereof under all conditions of filling of :the

reservoir.

2. A reservoir forholding a liquid ata variable level and under jpressureof a gas, comprising a hollowrbody formed essentially ofa thin wallin; 1.5 .r

the form' of a flattened spheroid with its bottom resting on the ground, a rigid ring above the ground and connected on the outside of the said wall substantially in the plane of maximum horizontal cross-section thereof, means between the ring and'the ground to anchor the ring with respect to the ground, the ring dividing the wall into upper and lower parts, the mean radius of curvature of the wall at each point being such that the compression forces which can arise in the wall under various filling conditions of the reservoir never exceed the resistance of the wall to buckling at such point, calculated from the wall thickness and the radius of curvature.

3. A reservoir for holding a liquid at a variable level and under pressure of a gas, comprising a hollow body formed essentially of a thin wall in the form of a flattened spheroid with its bottom resting on the ground, a rigid ring above the ground and connected on the outside of the said wall substantially in the plane of maximum horizontal cross-section thereof, means between the ring and the ground to anchor the ring with respect to the ground, the ring dividing the wall into upper and lower parts, the mean radius of curvature of the wall Cm'at each point being such that the horizontal compression force Nm which can arise in the wall under various con ditions of filling never exceeds aE 2 0,, lam-to where E is Hookes modulus, b is Poisson's coefllcient, e is the thickness of the wall and a is a safety factor.

4. A reservoir according to claim 3, in which a is at least 8.

5. A hollow structure for holding a liquid at variable level and a gas under pressure above said liquid, comprising a thin wall forming a container of curvilinear vertical and horizontal sections, a rigid belt secured to the outside of said container alon the horizontal section of maximum dimension thereof, the part of said structure located above said belt being constituted exclusively by a dome-shaped portion of said thin wall and having a horizontal dimension substantially greater than twice its greatest vertical dimension, the bottom part of said wall resting on the ground, and means wholly outside said wall anchoring said belt above the ground, the mean curvature of said wall, in the portions thereof adjoining said belt, being chosen to enable said wall to resist by itself such buckling stresses as may develop under particular filling conditions.

6. A structure according to claim 5 in which the means for anchoring said belt include at least one support anchored in the ground and a plurality of bracing and supportin means interposed between said support and said belt adapted to oppose translatory displacements of said belt parallel to the ground.

7. A structure according to claim 5 in which the means for anchoring said belt include at least one support anchored in the ground and a plurality of triangulated rods interposed between said support and said belt adapted to oppose translatory displacements of said belt parallel to the ground.

ALBERT IRENEE CAQUOT.

(References on following page) 9 REFERENCES CITED UNITED STATES PATENTS Number Name Date Horton Nov. 25, 1924 Horton Mar. 29, 1927 Number 10 Name Date Day May 15, 1928 Horton Nov. 1, 1932 Day Oct. 5, 1937 Pechstein May 2, 1939 Larson Sept. 29, 1942 Marner May 15, 1945 Boardman Mar. 11, 1947 

